# Solve system of equations by substitution online dating

System of equations is nothing but a system which contains more than one linear equations.This system of equations can be solved to arrive at the solution of the system.

For example, in the following sequence of row operations (where multiple elementary operations might be done at each step), the third and fourth matrices are the ones in row echelon form, and the final matrix is the unique reduced row echelon form.{\displaystyle \left[{\begin{array}{rrr|r}1&3&1&9\1&1&-1&1\3&11&5&35\end{array}}\right]\to \left[{\begin{array}{rrr|r}1&3&1&9\0&-2&-2&-8\0&2&2&8\end{array}}\right]\to \left[{\begin{array}{rrr|r}1&3&1&9\0&-2&-2&-8\0&0&0&0\end{array}}\right]\to \left[{\begin{array}{rrr|r}1&0&-2&-3\0&1&1&4\0&0&0&0\end{array}}\right]} Using row operations to convert a matrix into reduced row echelon form is sometimes called Gauss–Jordan elimination.Some authors use the term Gaussian elimination to refer to the process until it has reached its upper triangular, or (non-reduced) row echelon form.In linear algebra, Gaussian elimination (also known as row reduction) is an algorithm for solving systems of linear equations.It is usually understood as a sequence of operations performed on the corresponding matrix of coefficients.

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